Mr Bush allegedly made the pledge to Kathleen Kennedy Townsend, niece to US ex-President John F Kennedy.
The former president's office has not confirmed the report, with a spokesman saying he was checking.
Mr Bush, who held office from 1989 until 1993, has not endorsed Republican candidate Donald Trump.
If George HW Bush is indeed backing Hillary Clinton for president, that puts four of the five living presidents in the former secretary of state's camp.
George W Bush is the lone holdout - at least for now.
The Bush clan clearly isn't crazy about Donald Trump, given the way the New Yorker savaged Jeb in the Republican primaries.
It's worth noting, however, that the only family member with a political future - Texas Land Commissioner George P Bush - has endorsed his party's nominee.
The elder Bush does have a bit of a history with the Clintons. Although he and Bill Clinton were adversaries in the 1992 presidential contest, the two formed a friendship after the Democrat left office, co-operating on various charitable efforts.
It's unclear how much even an explicit Bush endorsement would help Mrs Clinton, given that most of the establishment Republicans who might break from the party have already done so.
This news might make it slightly easier for them to justify pulling the lever for the Democrat in November, however, rather than just sitting the vote out.
Neither has his son, Jeb Bush, who unsuccessfully competed for the Republican nomination, or other rivals in the race, Ted Cruz and John Kasich.
Ms Kennedy Townsend, a former Lieutenant Governor of Maryland, posted a photo on Facebook of a meeting with George HW Bush, alongside the caption: "The President told me he's voting for Hillary!"
Mr Bush's spokesman, however, was cautious.
"Those reporting how @GeorgeHWBush will vote this year, it's not clear anyone was there to verify KKT [Kathleen Kennedy Townsend]. Still checking, keep your powder dry," Jim McGrath wrote.
Source : http://www.bbc.com/news/world-us-canada-37416721